He told me that he is tired of hearing the same things "everyday." He said he feels numb to me saying I don't want to be alive.

No shit, who wants to be next to a person, invest time, money, effort, feelings in someone who have no respect from his own life and think about suicide every time

He gets more upset at the fact that he can't make me happy than my actual mental distress.

Yeah if he cant make the person he loves happy, how can he be happy

but all I expect is compassion and understanding.

You expect that but you don't give it to him. If you have compassion or understand him you would have changed, you would focus on things that make you happy, in solutions. You say that you understand him, but act totally different.

I don't need someone to fix me. I know that's my responsibility

It is not, you can't fix yourself, if you could you would have done it already.

I want to hear that my recent setbacks do not determine my worthiness of respect and love as a person.

I does determines, feelings steams from actions and not the contrary. You make actions the love flourish. If you don't, the love dies.

To hear that my partner feels kind of indifferent about my suicidal thoughts

He is not indifferent about it, he hates it, makes him sad, hurts him too. I have a friend with a girlfriend in the same situation, she had a bad creation while a kid and have a lot of distress symptoms. But now she is taking some meds and doing therapy, its controlled and she feels a little more alive, and they a little more happy.